Low Power Ecc for Eufs

1. A method of processing data, comprising: receiving a command to write information in a flash memory device; identifying a first element of an algebraic field; generating a plurality of lookup tables for multiplying the first element; multiplying the first element by a plurality of additional elements of the algebraic field, wherein the multiplication for each of the additional elements is performed using, an element from each of the lookup tables; encoding the information according to an error correction code (ECC) based on the multiplication; and programming the information in the flash memory device based on the encoding in response to the command.

2. The method of claim 1 , wherein the multiplying further comprises: splitting a second element of the algebraic field into a plurality of sub-elements, wherein a number of the sub-elements equals a number of the lookup tables; identifying a summation term from each of the plurality of lookup tables based on a corresponding sub-element from of the plurality of sub-elements; and computing a product of the first element and the second element by summing each of the summation terms.

3. The method of claim 2 , further comprising: splitting a third element of the algebraic field into another plurality of subsequent sub-elements, wherein a number of the additional sub-elements equals the number of the lookup tables; identifying a subsequent summation term from each of the plurality of lookup tables based on each of the plurality of subsequent sub-elements; and computing a product of the first element and the third element by summing each of the summation terms, wherein the information is encoded based on the product of the first element and the third element.

4. The method of claim 2 , wherein: each of the summation terms comprises a sum of products of the first element with a coefficient from a set of coefficients.

5. The method of claim 2 , wherein: a number of bits of the first element is equal to a number of bits of the second element.

6. The method of claim 2 , wherein: the summation term is identified from each of the plurality of tables using a corresponding sub-element of the plurality of sub-elements as an index.

7. The method of claim 1 , wherein: the number of the plurality of lookup tables is based at least in part on a number of bits of the first element.

8. The method of claim 1 , wherein: the encoding is based on an algebraic ECC scheme.

9. The method of claim 1 , further comprising: programming the encoded information to a memory.

10. A method of processing data, comprising: receiving a command to read information from a flash memory device; reading information from the flash memory device; identifying a first element of an algebraic field; generating a plurality of lookup tables for multiplying the first element; splitting a second element of the algebraic field into a plurality of sub-elements, wherein a number of the sub-elements equals a number of the lookup tables; identifying a summation term from each of the plurality of lookup tables based on each of the plurality of sub-elements; computing a product of the first element and the second element by summing each of the summation terms; decoding the information based on the product of the first element and the second element; and transmitting the information based on the decoding in response to the command.

11. The method of claim 10 , further comprising: splitting a third element of the algebraic field into another plurality, of subsequent sub-elements, wherein a number of the additional sub-elements equals the number of the lookup tables; identifying a subsequent summation term from each of the plurality of lookup to based on each of the plurality of subsequent sub-elements; and computing a product of the first element and the third element by summing each of the summation terms, wherein the information is encoded based on the product of the first element and the third element.

12. The method of claim 10 , wherein: the plurality of lookup tables are generated using a Gray code.

13. The method of claim 10 , further comprising: reading the information from a memory prior to the decoding.

14. The method of claim 10 , wherein: the decoding is based on an algebraic ECC scheme.

15. An apparatus for processing data, comprising: a processor; a memory; a table generation component configured to generate a plurality of lookup tables for multiplying a first element; a lookup component configured to split a second element of an algebraic field into a plurality of sub-elements, and identify a summation term from each of the plurality of lookup tables based on each of the plurality of sub-elements; a multiplication component configured to compute a product of the first element and the second element by summing each of the summation terms; an encoder configured to encode information based on the product of the first element and the second element or a decoder configured to decode the information based on the product of the first element and the second element; and a programming component configured to program the encoded information to the memory.

16. The apparatus of claim 15 , further comprising: a decoder configured to encode information based on an output of the multiplication component.

17. The apparatus of claim 15 , wherein: the multiplication component is configured to compute a plurality of products of the first element based on the lookup tables.

18. The apparatus of claim 15 , wherein: the plurality, of lookup tables are generated using a Gray code.

19. The apparatus of claim 15 , wherein: the lookup component is configured to identify the summation term from each of the plurality of tables using a corresponding sub-element of the plurality of sub-elements as an index.